Abrupt changes are ubiquitous in nature and modern engineering, such as the jump of cross sections at a tree fork, impact forces, mantle discontinuities [1]}, the interfaces of shock waves [2]}, and transient behaviors in signal processing [3]}, just to name a few.
These rapid changes correspond to a step-like jump or a localized spike, which can be described by a Heaviside function and a Dirac delta function, respectively.
In mechanical engineering, material and geometric discontinuities have been introduced to elastic structures for various outcomes, such as optimal mechanical properties in stepped beams [4]} and remarkable stretchability in flexible electronics [5]}, [6]}.
Made by decorating thin sheets with certain crease patterns, origami structures bring great potential in achieving compact folding [7]}, [8]}, [9]}, [10]}, [10]}, target geometries [12]}, [13]}, [14]}, [15]}, and tunable stiffness and stability in metamaterials [16]}, [17]}, [18]}.
However, it is challenging to study the mechanics of elastic structures with discontinuities (e.g. creases that correspond to \(C^0\)  continuity), which normally require cutting the structure and imposing matching conditions at the discontinuous interfaces [19]}, [20]}.
